Processing Math: Done
To print higher-resolution math symbols, click the
Hi-Res Fonts for Printing button on the jsMath control panel.
jsMath

Solution 2.3:1a

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 2.3:1a moved to Solution 2.3:1a: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
If we consider the squaring rule
-
<center> [[Image:2_3_1a.gif]] </center>
+
 
-
{{NAVCONTENT_STOP}}
+
 
 +
<math>\left( x-a \right)^{2}=x^{2}-2ax+a^{2}</math>
 +
 
 +
and move
 +
<math>a^{2}</math>
 +
over to the left-hand side, we obtain the formula
 +
 
 +
 
 +
<math>\left( x-a \right)^{2}-a^{2}=x^{2}-2ax</math>
 +
 
 +
 
 +
<math></math>
 +
 
 +
 
 +
With the help of this formula, we can rewrite (complete the square of) a mixed expression
 +
<math>x^{2}-2ax</math>
 +
to a obtain a quadratic expression,
 +
<math>\left( x-a \right)^{2}-a^{2}</math>
 +
.
 +
 
 +
The expression
 +
<math>x^{2}-2x</math>
 +
corresponds to
 +
<math>a=1</math>
 +
in the formula above and thus
 +
 
 +
 
 +
<math>x^{2}-2x=\left( x-1 \right)^{2}-1</math>

Revision as of 09:53, 12 September 2008

If we consider the squaring rule


x−a2=x2−2ax+a2 

and move a2 over to the left-hand side, we obtain the formula


x−a2−a2=x2−2ax 



With the help of this formula, we can rewrite (complete the square of) a mixed expression x2−2ax to a obtain a quadratic expression, x−a2−a2  .

The expression x2−2x corresponds to a=1 in the formula above and thus


x2−2x=x−12−1 

Retrieved from "http://wiki.math.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_2.3:1a"